Abstract
A set of binary relations closed with respect to some collection of operations on them forms an algebra called an algebra of relations. Algebras of relations can be viewed as partially ordered by the set-theoretic inclusion. Theory of algebras of relations is an essential part of modern algebraic logic and has numerous applications in semigroup theory. As a rule, operations on relations are specified using logical formulas. An operation on relations is called conjunctive if it can be defined by a first-order formula containing only conjunctions. The paper is devoted to the study of associative binary conjunctive operations on relations, that is, classes of semigroups of relations with conjunctive operations. A classification of conjunctive operations is carried out, all associative operations are identified, and problems of finding axiomatic characteristics for most of them are solved.